{"id":"https://openalex.org/W2016038303","doi":"https://doi.org/10.1137/s0036139902407303","title":"Stability of Stationary Solutions of the Multifrequency Radiation Diffusion Equations","display_name":"Stability of Stationary Solutions of the Multifrequency Radiation Diffusion Equations","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2016038303","doi":"https://doi.org/10.1137/s0036139902407303","mag":"2016038303"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139902407303","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902407303","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/15014445","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021208510","display_name":"Ole H. Hald","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ole H. Hald","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109242272","display_name":"A.I. Shestakov","orcid":null},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aleksei I. Shestakov","raw_affiliation_strings":["Lawrence Livermore National Laboratory"],"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Laboratory","institution_ids":["https://openalex.org/I1282311441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021208510"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.872,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68758699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"1","first_page":"175","last_page":"193"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6663984060287476},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.655498206615448},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5437057018280029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5352644920349121},{"id":"https://openalex.org/keywords/source-function","display_name":"Source function","score":0.5277127623558044},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4951154291629791},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.48495057225227356},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4753936529159546},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4752628207206726},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4526812434196472},{"id":"https://openalex.org/keywords/radiation","display_name":"Radiation","score":0.43416982889175415},{"id":"https://openalex.org/keywords/ideal-gas","display_name":"Ideal gas","score":0.4270135164260864},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1344781219959259},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13169556856155396},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13156113028526306},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09229537844657898}],"concepts":[{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6663984060287476},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.655498206615448},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5437057018280029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5352644920349121},{"id":"https://openalex.org/C2780187573","wikidata":"https://www.wikidata.org/wiki/Q3754592","display_name":"Source function","level":2,"score":0.5277127623558044},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4951154291629791},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.48495057225227356},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4753936529159546},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4752628207206726},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4526812434196472},{"id":"https://openalex.org/C153385146","wikidata":"https://www.wikidata.org/wiki/Q18335","display_name":"Radiation","level":2,"score":0.43416982889175415},{"id":"https://openalex.org/C30342001","wikidata":"https://www.wikidata.org/wiki/Q172280","display_name":"Ideal gas","level":2,"score":0.4270135164260864},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1344781219959259},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13169556856155396},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13156113028526306},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09229537844657898},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139902407303","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902407303","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:osti.gov:15014445","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/15014445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:15014445","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/15014445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1499163627","https://openalex.org/W1992459887","https://openalex.org/W2016423519","https://openalex.org/W2029627128","https://openalex.org/W2050815633","https://openalex.org/W2092168115","https://openalex.org/W2786634864","https://openalex.org/W2795744704","https://openalex.org/W3021722416","https://openalex.org/W3187596537"],"related_works":["https://openalex.org/W3013650182","https://openalex.org/W4249605382","https://openalex.org/W4313491656","https://openalex.org/W3279617","https://openalex.org/W2989283631","https://openalex.org/W4309070540","https://openalex.org/W2801126415","https://openalex.org/W2586961741","https://openalex.org/W2057152511","https://openalex.org/W2111084772"],"abstract_inverted_index":{"A":[0,11],"nondimensional":[1],"model":[2],"of":[3,25,28,32,73],"the":[4,23,26,29,40,48,69,74],"multifrequency":[5],"radiation":[6,41],"diffusion":[7],"equation":[8],"is":[9,17,45],"derived.":[10],"single":[12],"material":[13],"ideal":[14],"gas":[15],"equation-of-state":[16],"assumed.":[18],"Opacities":[19],"are":[20,50,59,65],"proportional":[21],"to":[22],"inverse":[24],"cube":[27],"frequency.":[30],"Inclusion":[31],"stimulated":[33],"emission":[34],"implies":[35],"a":[36],"Wien":[37],"spectrum":[38],"for":[39],"source":[42],"function.":[43],"It":[44],"shown":[46],"that":[47,56],"solutions":[49,58,64,72],"uniformly":[51],"bounded":[52],"in":[53],"time":[54],"and":[55],"stationary":[57],"stable.":[60],"The":[61],"spatially":[62,70],"independent":[63],"asymptotically":[66],"stable,":[67],"while":[68],"dependent":[71],"linearized":[75],"equations":[76],"approach":[77],"zero.":[78]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
